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So would you sell the call and buy the put and not buy or sell any stock?

Did you mean long the shares and then short the call and put? Or did you mean go long, sell call and buy put? I still don't see why you would by the shares?

I'm helping a friend here with one of his MBA derivatives questions so maybe you guys can shed some light on what I can't. A European call option and put option on a stock both have a strike price of $20 and an expiration dates in 3 months. Both sell for $3. The risk-free interest rate is...